The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  0  1  1  1  1  1  X  1  1  X  X  0  1  X  1  X  X  0  0  0  X  1  X  1  1
 0  1  0  0  0  0  0  0  0  1 X+1  1  1  1 X+1 X+1  X X+1  0  1  X  X  0  1  1 X+1  1  1  X  1  1  0  X  1  1  0 X+1  0
 0  0  1  0  0  0  1  1  1  1  1  0  X  0  0  X X+1 X+1  X  X  0 X+1  1  1  1  0 X+1  1  1  0  1  X  1 X+1  1  1  0  0
 0  0  0  1  0  1  1  0  1  0  0  1  1  1 X+1  X  1  1  1  0  X  X  0 X+1 X+1  0  X X+1  1 X+1  X  1  X  1  X  1 X+1  0
 0  0  0  0  1  1  0  1  1  0  1  0  X  1  1  0 X+1  X  0 X+1 X+1  0  1  X X+1 X+1  X  1  X  0 X+1  1 X+1 X+1  1  X X+1  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  X  0  X  0  0  X  X  0  0  0  0  0  X  X  X  0  X  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  0  X  X  0  0  X  X  0  X  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  0  0  X  X  0  X  0  0  X  0  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  X  X  0  0  0  X  X  0  0  X  X  0
 0  0  0  0  0  0  0  0  0  X  X  0  0  X  X  X  X  0  X  0  X  0  0  X  0  X  X  X  X  0  X  0  0  0  0  X  X  X

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+61x^26+90x^27+269x^28+420x^29+711x^30+820x^31+1183x^32+1574x^33+1831x^34+2266x^35+2591x^36+2924x^37+2921x^38+3058x^39+2740x^40+2444x^41+2011x^42+1566x^43+1155x^44+732x^45+553x^46+360x^47+236x^48+94x^49+97x^50+30x^51+17x^52+4x^53+7x^54+2x^55

The gray image is a linear code over GF(2) with n=76, k=15 and d=26.
This code was found by Heurico 1.16 in 55.6 seconds.